If A is a matrix of order n such that `A^(T)A=I` and X is any matric such that `X=(A+I)^(-1) (A-I)`, then show that X is skew symmetric matrix.

If the matrix A=((2,3),(4,5)) , then show that A-A^(T) is a skew-symmetric matrix.

If A=[[3,-4], [1,-1]] , show that A-A^T is a skew symmetric matrix.

If A is a square matrix of order n and A A^T = I then find |A|

If A is any square matrix such that A+I/2 and A-I/2 are orthogonal matrices, then

If A is a skew-symmetric matrix of odd order n , then |A|=0

If A=[a_(i j)] is a square matrix such that a_(i j)=i^2-j^2 , then write whether A is symmetric or skew-symmetric.

If A is a skew-symmetric matrix of odd order n , then |A|=O .

If I_n is the identity matrix of order n, then rank of I_n is

If A=[a_(i j)] is a square matrix of even order such that a_(i j)=i^2-j^2 , then (a) A is a skew-symmetric matrix and |A|=0 (b) A is symmetric matrix and |A| is a square (c) A is symmetric matrix and |A|=0 (d) none of these

For, a 3xx3 skew-symmetric matrix A, show that adj A is a symmetric matrix.